Plane on a coneyor belt
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yes it is indeed. only that it is work (and my boss) calling at the moment
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If nothing else thats a pretty funny cartoon.
If you ever recover the will to live, i'm interested to know where the flaw is in my argument
You lost me with your thing about friction jakob...
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Remus, The terms aren't defined nearly precisely enough.
I think we can probably agree that conveyor speed would be that speed as observed by somone at a fixed point at the side of the conveyor. I think we can also agree that the plane's speed would be its forward motion through the air (assuming no wind and again relative to a fixed observer).But what the heck is "wheel speed"? Do you mean the speed at the bottom of the wheel...where it makes contact with the conveyor? Is that relative to a fixed observer or relative to the conveyor it is rolling over? Do you mean the speed of the hub (which would be the same as the plane's speed)? Or do you mean the speed of the wheel at the TDC (which would not be simply a negative value of the speed at the bottom, because you would need to add any forward motion of the plane to that).
Unless you are clear about your frames of reference you can make some very basic errors...like the equation. The way it is phrased creates a circular argument that allows the plane no forward motion. All it says is the plane remains static because it's static, therefore it can't take off. No kidding? That's why you end up with two irreconcilable functions...because you artificially injected a plane speed (+100) into an argument that prohibited a plane speed.
Jakob, of course the skateboard will fall off if it has no forward power. I thought we were discussing a plane that was powering forward? The skateboard however will not move backwards at the same speed as the treadmill.
If you don't believe me, I repeat, place a sheet of A4 on the table. Place a roll of tape on top of it and pull the sheet back at something like treadmill speed.The treadmill will transport the skateboard backwards...but only by as much as friction will allow, it's not like transporting it tied down on the back of a truck.
As I said before, this friction will remain constant regardless of the speed of the treadmill. Pulling that paper faster is not going to make the roll of tape go backwards faster...in fact it might even stand still or move forwards.All the business regarding the speed of the wheels is irrelevant...it has no direction, therefore can't counter any movement. All that is happening is that the wheels are storing potential energy so that they would rocket the skateboard forwards if the treadmill were to suddenly stop. There is no equation you can quote that will demonstrate that you need more force to keep the skateboard static as the treadmill increases its speed. The only point of contact between the two is the bottom of the wheels and the only force at play is friction. Friction is a function of the coefficient of friction and weight. Speed has nothing to do with it. Yes the wheels will get hotter with increased speed. That's simply because the amount of kinetic energy being transferred is outstripping the ability of the atmosphere to dispel the resulting heat. It has no more effect on the motion of the skateboard than if you were to siphon off that energy some other way, pass it through a dynamo and point an electric fire at the skateboard.
Increasing the speed of the treadmill has the same effect as increasing the speed of the paper under the tape...none at all.You made an analogy earlier to someone on a bike hanging off the back of a moving vehicle and stated that the force on their arm would increase the faster that vehicle went. No it wouldn't. It would only increase by two means a) if they were subjected to increased air resistance, or b) while the vehicle was actually accelerating. Once it reached a higher speed the pull on the cyclist's arm would be exactly the same as before.
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...or putting it very much simpler:-
Remus, you already agreed that the plane would be able to take off in your first example. It could take off because the speed of the conveyor is irrelevant.Would you mind explaining to me what is different in the second example? Irelevant means irrelevant....whether the conveyor is travelling at a constant speed or accelerating in direct ratio to the wheel speed or anything else in the Universe.
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I just thought about the wheel of my brother's racing cycle. if I spin it as fast as I can, it will take a minute to come to a halt (due to the small amount of frictional resistance).
so I agree with you, that practically, it is impossible to use this tiny amount of force applyable to stop the plane from moving forward.
but I allways had the impression, that the bycicle wheel lost most of it's speed at the beginning. I believe, that the slow down does not happen in a linear way, but in a curve. that would mean, that speed does matter!
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To try and define what i meant by wheel speed, i suppose youd call it the rotational speed of the wheel multiplied by the circumfrence of the wheel.
In the first question what happens to the wheels is entirely possible. In the second question what is happening to the wheels is entirely impossible.
EDIT:I started to write out a big long reply, but i hit a mental blank. Give me a while to ponder. You may have won me over alan
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Jakob, i find it hard to believe you can accurately judge the speed of a wheel just by looking at it...
And speed does play a part in air resistance, but not in frictional resistance.
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well that was just my objective observation.
but for friction (or lets call it Rolling resistance) speed does play a part!
http://en.wikipedia.org/wiki/Rolling_resistance#cite_note-Hibbeler-0@unknownuser said:
Additional factors include wheel radius, and forward speed
I tried to do some calculations. I used the Eurofighter 2000 Typhoon as an example (because it is the best fighter jet Europe can provide
).according to the formula provided by wikipedia, the rolling resistance of the Eurofighter 2000 is:
(I asumed the jet's tires to be equivalent to a Low-resistance car tire on a smooth road)1,53 kN
the thrust of the jet engines (without afterburner) is:
60 kN
unfortunately I did not find a formula that contained a speed-variable...
Can someone check this? the rolling resistance seems a bit too high to me (in relation to the thrust of the engines...) -
@remus said:
To try and define what i meant by wheel speed, i suppose youd call it the rotational speed of the wheel multiplied by the circumfrence of the wheel.
That's where you are going wrong. All other observations have been made from the point of view of a static observer at the side of the conveyor belt.
If you only allow for a single "wheel speed" you will only achieve that by keeping the wheel absolutely stationary relative to such an observer and having it spin on the spot. You have, in effect tethered the plane before it even gets going. Either that or you have suddenly switched from being a static observer to one travelling alongside the plane, completely altering the frame of reference.In reality, to a static observer the wheel speed at the top of the wheel would be the sum of your rotational speed plus any forward motion of the aircraft.
At the bottom of the wheel it would be the rotational speed (obviously minus, if we are using vectors) minus the speed of the aircraft.The plane can only move in either direction if the two opposing speeds differ from one another, relative to a static point. If they are held to be the same, then they cancel each other out and the wheel (and plane) ain't going nowhere.
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Alan's right. There's no complicated physics required (especially crock physics) to resolve it. The wheels on the plane are irrelevant- they have negligible effect on the forward motion of the plane. In fact that's the whole point of the wheels, unlike driven car wheels, plane wheels are there to isolate the plane from it's surroundings- i.e. to reduce the friction between the plane and the ground to the point that it is negligible.... until the brakes are applied.
The wheels are irrelevant, the conveyor belt is irrelevant, the lift of the plane is irrelevant, the crux of the problem is simply: do jet planes propel themselves forward when their jet engines are fired up? Of course they do, whether they're on land, in the air or in a vacuum (well rocket engines in the last case).
Now if the plane was in a wind tunnel which could match the velocity of the plane's jet engines, that would be a different problem altogether (but just as easily solved).
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